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We present terahertz (THz) measurements and density functional theory (DFT) calculations of two amino acid crystals: dl-norleucine and dl-methionine. Their molecular structures are very similar and therefore also their crystal structures. We report the absorption spectra for both amino acids, which have a strong resonance at 1.87 THz in dl-norleucine and 1.94 THz in dl-methionine. In addition, we find a higher frequency resonance at 2.49 THz in dl-methionine, which has no corresponding mode in dl-norleucine. The experimental data are supported by DFT calculations, which show that the origin of the two strongest vibrational modes in dl-norleucine and dl-methionine are based on the same underlying vibrational motions, whereas the 2.49 THz resonance in dl-methionine is due to the motion of the sulfur atom, which is not present in dl-norleucine.